Abstract

A one-dimensional hydrodynamic model that mimicked a two-dimensional fluidized granular system with a vibrating and without gravity, and exhibited a phase separation, was investigated. The objective was to achieve an explicit derivation of the van der Waals normal form (VDWNF) from the hydrodynamic model. The VDWNF was deduced close to the critical point by means of an adiabatic elimination the temperature. The VDWNF was the equation that described the slow dynamics of the system and predicted the qualitative behavior in different regions of parameters. The origin of the effective viscosity and the spatial saturation at the onset of the bifurcation were also discussed.